110_networks.Rmd

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[Introduction to Data Analysis](index.html "Course index")

# 11. Networks

Networks are a common aspect of your daily life, and since you have been logging your network of friends and colleagues on services like Facebook or [LinkedIn][li-inmaps], there are tons of data available. There is also a large amount of research on networks with [tough questions][cs-contagion], such as the analytical difference between homophily (connecting to those like us) and contagion (becoming like our connections). We will stick to description and simple measures of influence.

[li-inmaps]: http://inmaps.linkedinlabs.com/ "LinkedIn Maps ('Your professional world. Visualized.')"
[cs-contagion]: http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/773.html "Knights, Muddy Boots, and Contagion; or, Social Influence Gets Medieval (Cosma Shalizi)"

There are several software options for network analysis, like [Gephi][gephi], [Pajek][pm-pajek] or [VOSON][voson] (for hyperlink networks). We will stay in R and use the `sna` and `igraph` libraries, which use [different but compatible formats][lb-intergraph] to store network data. Some examples will be taken from [Baptiste Coulmont's graphs][bc-igraph] of small cliques.

[bc-igraph]: http://coulmont.com/index.php?s=igraph "Examples of igraph plots (Baptiste Coulmont)"
[lb-intergraph]: http://groupefmr.hypotheses.org/363 "Jongler avec les objets R, le package intergraph (Laurent Beauguitte)"
[gephi]: https://gephi.org/ "Gephi software"
[voson]: http://voson.anu.edu.au/ "VOSON software (Virtual Observatory for the Study of Online Networks)"
[pm-pajek]: http://quanti.hypotheses.org/512/ "Analyse des réseaux : une introduction à Pajek (Pierre Mercklé)"

## A random network

```{r packages, echo = FALSE, message = FALSE}
# Load packages.
packages <- c("intergraph", "GGally", "ggplot2", "network", "RColorBrewer", "sna")
packages <- lapply(packages, FUN = function(x) {
  if(!require(x, character.only = TRUE)) {
    install.packages(x)
    library(x, character.only = TRUE)
  }
})
```

We'll start with [simulating a random network][fs-sim] of $n = 30$ individuals (`ego`), for which we simulate a bidirectional friendship relationship: if individual 'Ego' is a friend of individual 'Alter', then the reciprocal is true. Each individual has the possibility to associate with any other individual in the network, resulting in a network matrix of $30^2 = 900$ rows, with one extra row per individual that connects it to itself ($n-n$) and that will be ignored when generating relationships. The result is the `rnet` dataset.

[fs-sim]: http://www.econometricsbysimulation.com/2012/10/simulating-social-network-data.html "Simulating Social Network Data (Francis Smart)"

```{r smart-random-network-1}
# Set network size.
n = 30
# Create n series of n.
ego = rep(1:n, each = n)
# Create n sequences of n.
alter = rep(1:n, times = n)
# Default to no friendship between ego and alter.
friendship = 0
# Assemble dataset.
rnet = data.frame(ego, alter, friendship)
# First rows.
head(rnet)
```

To generate random relationships, we draw from a binomial distribution where the probability of a friendship is artificially set to $Pr(friendship) = .15$. The result is a network that displays approximately 15% of all possible `friendship` ties in the `rnet` dataset.

```{r smart-random-network-2}
# Probability of friendship tie.
conDen <- .15
# Assign ties to random nodes.
for (i in 1:n)
  for (ii in (i+1):n)
    if ((rbinom(1, 1, conDen) == 1) & (i != ii)) {
      rnet$friendship[(rnet$ego ==i  & rnet$alter == ii)] = 1
      rnet$friendship[(rnet$ego ==ii & rnet$alter == i )] = 1
      }
# Inspect random network ties.
summary(rnet)
```

The network is drawn with the [`ggnet` function][gh-ggnet]. The plot function processes the subset of the `rnet` data frame for which the `friendship` variable indiciates that there is a relationship to draw. The ties are undirected: there are no arrows between the nodes because the friendship ties are strictly reciprocal.

[gh-ggnet]: https://github.com/briatte/ggnet

```{r smart-randomnetwork-3-auto, message = FALSE, warning = FALSE, tidy = FALSE}
# Form network object.
net = network(rnet[rnet$friendship == 1, ], directed = FALSE)
net
# Plot random network.
ggnet(net,
      label = TRUE,
      color = "white")
```

This function is used in the next pages to plot a few social networks. You can train yourself by plotting fictional networks, like the one below using [the _Grey's Anatomy_ network by Gary Weissman][gw-grey], or turn to Solomon Messing's analysis of [U.S. student affiliations][sm-student] for a real-world example of network data.

[sm-student]: https://solomonmessing.wordpress.com/2012/09/30/working-with-bipartiteaffiliation-network-data-in-r/
[gw-grey]: http://www.r-bloggers.com/grey%E2%80%99s-anatomy-network-of-sexual-relations/

```{r greys-anatomy-auto, message = FALSE, warning = FALSE, tidy = FALSE, cache = TRUE}
# Locate data.
link = "http://www.babelgraph.org/data/ga_edgelist.csv"
file = "data/ga.network.csv"
# Download data.
if(!file.exists(file)) download(link, file, mode = "wb")
# Create network.
net = network(read.csv(file), directed = FALSE)
# Plot network.
ggnet(net, 
      label = TRUE, 
      color = "white", 
      top8 = TRUE, 
      size = 18,
      legend.position = "none")
```

The next pages make more use of the `ggnet` function with Twitter data and word associations plotted as network ties.

> __Next__: [Influence](111_influence.html).